This invention relates to a single-polarization single-mode optical fiber utilized in a coherent optical transmission system, optical measurement, a coupling with an integrated circuit, etc.
When the propagation constants of light of HE.sub.11 mode which is polarized in the directions of two orthogonal major axes of an optical fiber is denoted by .beta..sub.x and .beta..sub.y respectively, the modal birefrigence B is given by EQU B=(.beta..sub.x -.beta..sub.y)/k (1)
where k is called the wave number of light transmitting through vacuum and expressed by an equation k=2.pi./.lambda.(.lambda. represents the wavelength of light in vacuum). It is well known that the modal birefringence B should be larger than about 10.sup.-6 in order to prevent linearly polarized state from being disturbed by such external forces as bending force or pressure when linearly polarized light is incident in the direction of the major axis of an optical fiber (see for example R. Ulrich et al "Bending-induced birefringence in single-mode fibers" Optics Ltt. Vol. 5, No. 6 pp. 273-275, 1981). Consequently, it has been proposed to increase the modal birefringence by providing a noncircular core at the center of a clad (see. C. Yah, "Elliptical dielectric waveguides", Journal of applied Physics. Vol. 33. No. 11, pp. 3235-3243, 1962) or by disposing a pair of second clads on both sides of a central core, the second clads being made of a material having different thermal expansion coefficient as that of the central core and a clad, so as to apply asymmetrical stress upon the central core (see Japanese patent application No. 4587/1981 invented by Miyagi and having a title of the invention "Method of manufacturing an internal stress birefringence single-mode optical fiber").
The modal birefringence B of an optical fiber having a noncircular core is expressed by the following equation EQU B=(.beta..sub.xo -.beta..sub.yo)/k+P.multidot.(.sigma..sub.x -.sigma..sub.y) (2)
where .beta..sub.xo and .beta..sub.yo represent propagation constants under a no stress condition, .sigma..sub.x and .sigma..sub.y are principal stresses (kg/mm.sup.2) in the directions of major axes and P represents a photoelastic coefficient of quartz glass given by EQU P=3.36.times.10.sup.-5 (mm.sup.2 /kg) (3)
The first term of equation (2) is called geometrical anistropy B.sub.g, while the second term is called stress-induced birefringence B.sub.s. Now, suppose that the ellipticity .epsilon. of the elliptical optical fiber is given by an equation EQU .epsilon.=1-b/a (4)
where a represents a major radius of the ellipse and b a minor radius thereof.
The geometrical anisotropy B.sub.g and the stress induced birefringence B.sub.s of an optical fiber having an ellipticity .epsilon.=0.4 and a relative refractive index difference of .DELTA.=0.6% are calculated as B.sub.g =1.2.times.10.sup.-5 and B.sub.s =3.1.times.10.sup.-5, whereas the modal birefringence is shown by EQU B=B.sub.g +B.sub.s =4.3.times.10.sup.-5 ( 5)
The delay times per unit length of orthogonal polarization modes of a single-polarization optical fiber are ##EQU1##
Under these conditions, the difference D between the delay times (polarization mode dispersion) per unit length of the two polarization modes is given by the following equation ##EQU2## where c represents the velocity of light in vacuum. From equations (1) and (2) the polarization mode dispersion D is given by the following equation ##EQU3##
In equation (9), the first term on the righthand side represents the delay time difference in the absence of the asymmetrical stress, while the second term represents the delay time difference caused by the stress and these differences are defined as D.sub.g and D.sub.s respectively. In the case of an optical fiber having an elliptical core, D.sub.g is given by ##EQU4## where n.sub.1 represents the refractive index and F(V) a function determined by a normalized frequency V and the ellipticity .epsilon.. The polarization mode dispersion caused by stress can be calculated experimentally.
For example, where .DELTA.=0.6%, .epsilon.=0.4, V=0.9V.sub.c (where V.sub.c shows the cut off frequency of an optical fiber having an elliptical core), since F(V)=0.16 EQU D.sub.g =11 (ps/km) (11)
Since B.sub.s =3.1.times.10.sup.-5 EQU D.sub.s =B.sub.s /c=103 (ps/km) (12)
Accordingly, the polarization mode dispersion is given by EQU D=D.sub.g +D.sub.s =114 (ps/km) (13)
The polarization mode dispersion of a single-polarization optical fiber applied with asymmetrical stress in the direction of the x axis by a pair of fan shaped stress applying parts (see Hosaka et al "Single-polarization optical fiber having asymmetrical refractive index pits" (OQE81-22, P. 43-48, 1981) is measured as follows. In this case, it is assumed that the core is made of GeO.sub.2 --SiO.sub.2, the stress applying parts are made of B.sub.2 O.sub.3 --SiO.sub.2 and the clad is made of SiO.sub.2, that the core has a relative refractive index difference .DELTA.=0.61%, an ellipticity .epsilon.=0.07, that the specific refractive index difference of the stress applying members .DELTA..sub.s =-0.44%, and the outer diameter of the clad 2d=160 microns.
As will be described later with reference to the accompanying drawings, a single polarization optical fiber having a large modal birefringence B which was manufactured for the purpose of stabilizing the polarization characteristic against external disturbance has a large polarization mode dispersion.
In such an optical fiber, where a slight mode coupling exists between two polarization modes a large polarization mode dispersion results thus greatly degrading the propagation characteristic in a coherent optical transmission system or the like.